doi: 10.17586/2226-1494-2015-15-4-603-607


ASPHERICAL SURFACES APPROXIMATION IN AUTOMATED DESIGN OF OPTICAL SYSTEMS

T. V. Ivanova, G. E. Romanova, T. I. Zhukova, Y. E. Stepanov, I. I. Bondar, R. O. Dantsaranov


Read the full article  ';
Article in Russian

For citation: Ivanova T.V., Romanova G.E., Zhukova T.I., Stepanov Ya.E., Bondar I.I., Dantsaranov R.O. Aspherical surfaces approximation in automated design of optical systems. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2015, vol.15, no. 4, pp. 603–607.

Abstract
Subject of Research. The paper deals with the problems of higher order aspherical surfaces approximation using different equation types. The objects of research are two types of equations for higher order aspherical surfaces description used in different software for optical systems design (SАRО, OPAL, ZEMAX, CODE-V, etc.) and dependent on z-coordinate or on a radial coordinate on the surface. Conversion from one type of equations to another is considered in view of application in different software for optical systems design. Methods. The subject matter of the method lies in usage of mean square method approximation for recalculation of high-order aspherical surface. Iterative algorithm for recalculation is presented giving the possibility to recalculate coefficients for different types of equations with required accuracy. Recommendations are given for choosing recalculation parameters such as the number of result equation coefficients, the number of points for recalculation and point allocation on a surface. Main Results. Example of recalculation for aspherical surface and accuracy estimation, including result aberration comparison between initial surface and recalculated surface are presented. The example has shown that required accuracy of surface representation was obtained. Practical Relevance. This technique is usable for recalculation of higher order aspherical surfaces in various types of software for optical systems design and also for research of optimal higher order aspherical surfaces description.

Keywords: aspherical surfaces, approximation, least-square method, optical system design software, ZEMAX.

References
1. Rusinov M.M. Nesfericheskie Poverkhnosti v Optike. Raschet, Izgotovlenie i Kontrol' [Non-Spherical Surface in Optics. Calculation, Manufacture and Control]. Moscow, Librokom Publ., 2010, 296 p.
2. Schroder G., Treiber H. Technische Optik. 9th ed. Wurzburg, Vogel Buchverlag, 2002.
3. Zhou X.-Q., Bryan N.K.A., Koh Soon S. Single aspherical lens for deastigmatism, collimation, and circularization of a laser beam. Applied Optics, 2000, vol. 39, no. 7, pp. 1148–1151.
4. Fuchs U., Moritz J. Flexible and robust beam shaping concepts with aspherical surfaces. Proceedings of SPIE – The International Society for Optical Engineering, 2014, vol. 9293, art. 92930B. doi: 10.1117/12.2072613
5. Hall P.R. Use of aspheric surfaces in infrared optical designs. Optical Engineering, 1987, vol. 26, no. 11, pp. 1102–1111. doi: 10.1117/12.7974202
6. Lerner S.A., Sasian J.M. Use of implicitly defined optical surfaces for the design of imaging and illumination systems. Optical Engineering, 2000, vol. 39, no. 7, pp. 1796–1801. doi: 10.1117/1.602559
7. Kross J., Oertmann F.W., Schuhmann R. On aspherics in optical systems. Proceedings of SPIE – The International Society for Optical Engineering, 1986, vol. 655, pp. 300–309. doi: 10.1117/12.938437.
8. Schaub M.P. The Design of Plastic Optical Systems. Bellingham, SPIE Press, 2009, 226 p.
9. Scott P. Recent developments in the measurement of aspheric surfaces by contact stylus instrumentation. Proceedings of SPIE – The International Society for Optical Engineering, 2002, vol. 4927. doi: 10.1117/12.464331.
10. Jo J.S., Trolinger J.D., Lal A.K. An instrument for inspecting aspheric optical surfaces and components. Proceedings of SPIE – The International Society for Optical Engineering, 2010, vol. 7791, art. 779106. doi: 10.1117/12.862139.
11. Hanayama R. A trial for a reliable shape measurement using interferometry and deflectometry. Proceedings of SPIE – The International Society for Optical Engineering, 2014, vol. 9203, art. 92030D-1. doi: 10.1117/12.2060353.
12. Besenmatter W. Weight optimization in lens design. Proceedings of SPIE – The International Society for Optical Engineering, 2005, vol. 5962, no. 2, art. 5962OU. doi: 10.1117/12.625059.
13. Rodionov S.A., Shekhonin A.A. Matematicheskie modeli opticheskikh poverkhnostei pri avtomatizirovannom proektirovanii [Mathematical models of the optical surfaces at the automated designing]. Izv. Vuzov. Priborostroenie, 1996, vol. 39, no. 2, pp. 99–103.
14. Zverev V.A., Romanova G.E. Nesfericheskie poverkhnosti i problemy ikh approksimatsii [Non-spherical surfaces and problems of their approximation]. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2004, no. 15, pp. 158–174.
15. Zverev V.A., Krivopustova E.V. Optotekhnika Nesfericheskikh Poverkhnostei. Uchebnoe Posobie [Optical Engineering of Aspherical Surfaces. Textbook]. St. Petersburg, SPbSU ITMO Publ., 2006, 203 p.
16. ZEMAX Optical Design program: User’s Guide. 2014, 766 p.
17. Zverev V.A., Romanova G.E. Nesfericheskie poverkhnosti v optike i problemy ikh approksimatsii [Non-spherical surface in optics and problems of approximation]. Opticheskii Zhurnal, 2004, vol. 71, no. 11, pp. 29–40.


Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2024 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.

Яндекс.Метрика